Tests on combined projection/forward differencing integration for stiff photochemical family systems at long time step

Elliott, Scott; Richard, P Turco; Jacobson, Mark Z.

doi:10.1016/0097-8485(93)80034-b

Cited by 45 publications

(12 citation statements)

References 58 publications

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“…The coupled system (20)- (21) is integrated locally from t n to t n+1 using DVODE [12]. The initial conditions correspond to the scalar values at time level t n , and the integrations are performed independently at the cell centers where the scalar fields are defined.…”

Section: N6mentioning

confidence: 99%

A Semi-implicit Numerical Scheme for Reacting Flow

Knio¹,

Najm²,

Wyckoff³

1999

Journal of Computational Physics

158

145

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Section: N6mentioning

confidence: 99%

A Semi-implicit Numerical Scheme for Reacting Flow

Knio¹,

Najm²,

Wyckoff³

1999

Journal of Computational Physics

158

145

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“…The chemistry model was developed over a period of years [Turco andWhitten, 1974, 1977;Turco, 1975;Elliott et al, 1993Elliott et al, , 1995Zhao, 1995]. A highly stable numerical scheme allows computational speed to be maintained at a fixed time step as large as 2 hours.…”

Section: Chemistry Componentmentioning

confidence: 99%

“…That leads to the problem of determining how to partition each family among its member species. Our approach utilizes a unique multistep "projection" and partitioning scheme [Elliott et al, 1993[Elliott et al, , 1995Zhao, 1995] that ensures computational stability even with large time steps. Basically, the family continuity equation is solved explicitly using chemical rates averaged over the time step.…”

Section: Chemistry Componentmentioning

confidence: 99%

Aerosol‐induced chemical perturbations of stratospheric ozone: Three‐dimensional simulations and analysis of mechanisms

Zhao¹,

Turco²,

Kao³

et al. 1997

J. Geophys. Res.

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Abstract. An atmospheric general circulation model is coupled with a stratospheric photochemical model to simulate the chemical/dynamical perturbations associated with background and volcanically perturbed aerosols in the lower stratosphere. The present work focuses on short-term anomalies at middle and high latitudes in the northern hemisphere, where large ozone depletions have been observed in late winter and early spring, particularly following the eruption of Mount Pinatubo. Five fully coupled simulations are analyzed, corresponding to a control case with only gas phase chemistry, and cases including heterogeneous chemistry on background aerosols, on E1 Chich6n-type, and on Pinatubo-type aerosols. It is found that heterogeneous reactions occurring on sulfate aerosols (background or postvolcanic) can strongly perturb the chemical partitioning in the lower stratosphere, leading to significant ozone depletion through enhanced chlorine, bromine, and odd-hydrogen catalytic cycles. In the Arctic lower stratosphere, the maximum zonal and March monthly mean local ozone reductions (with respect to the control case) can exceed 15% for the background aerosol case, 40% for the E1 Chich6n case, and 50% for the Pinatubo case. The corresponding zonal mean total column ozone decreases are roughly 5% and 15% for the background and volcanic aerosol cases, respectively. In the most extreme case tested (post-Pinatubo), a large ozone depletion below 30 mbar is offset to some extent by an ozone increase above that level. The results of a sensitivity study (in which the aerosols are distributed closer to the tropics, as might occur early after an eruption at low latitude) lead to relatively small total ozone depletions at northern high latitudes, and small ozone increases in the tropical lower stratosphere. The reduced impact on total ozone at high latitudes is associated both with local ozone increases above 30 mbar and with poleward transport of enhanced ozone from the tropical lower stratosphere. The ozone increase at low latitudes is the net result of compensating changes in the catalytic destruction cycles involving odd-nitrogen and chlorine species activated by heterogeneous processes at the low temperatures and abundant sunlight found near the tropical tropopause. Our simulations indicate that ozone variations triggered by volcanic injections of aerosols depend on the global distribution as well as the abundance of the particles and their evolution over time, and on the initial dynamical-radiative-chemical state of the atmosphere, which itself exhibits large seasonal and interannual variability.

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“…The equivalent (summed) family rate equations can then be solved using relatively simple algorithms. Elliott et al [1993Elliott et al [ , 1995Elliott et al [ , 1996 demonstrated that this minimatrix approach can be highly efficient and accurate in many situations involving stratospheric and tropospheric chemical systcms. However, on a global grid the explicit family solutions can bccomc unstable in certain regimes, leading to substantial errors (see below).…”

Section: Introductionmentioning

confidence: 99%

“…In one approach, researchers have sought to reduce the effective size of the JacobJan system matrix, thus reducing the number of computations needed to carry out the required matrix inversions. Elliott et al [1993Elliott et al [ , 1995Elliott et al [ , 1996 family. Owing to the longer lifetime of the family compared to its member species, the family rate equation can often be solved using standard algorithms, including low-order explicit numerical schemes, whereas similar solutions of the species rate equations would be unstable.…”

Section: Introductionmentioning

confidence: 99%

A new family Jacobian solver for global three‐dimensional modeling of atmospheric chemistry

Zhao¹,

Turco²,

Shen³

1999

J. Geophys. Res.

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Abstract. We present a new technique to solve complex sets of photochemical rate equations that is applicable to global modeling of the troposphere and stratosphere. The approach is based on the concept of "families" of species, whose chemical rate equations are tightly coupled. Variations of species concentrations within a family can be determined by inverting a linearized Jacobian matrix representing the family group. Since this group consists of a relatively small number of species the corresponding Jacobian has a low order (a minimatrix) compared to the Jacobian of the entire system. However, we go further and define a super-family that is the set of all families. The super-family is also solved by linearization and matrix inversion. The resulting Super-Family Matrix Inversion (SFMI) scheme is more stable and accurate than common family approaches. We discuss the numerical structure of the SFMI scheme and apply our algorithms to a comprehensive set of photochemical reactions. To evaluate performance, the SFMI scheme is compared with an optimized Gear solver. We find that the SFMI technique can be at least an order of magnitude more efficient than existing chemical solvers while maintaining relative errors in the calculations of 15% or less over a diurnal cycle. The largest SFMI errors arise at sunrise and sunset and during the evening when species concentrations may be very low. We show that sunrise/sunset errors can be minimized through a careful treatment of photodissociation during these periods; the nighttime deviations are negligible from the point of view of acceptable computational accuracy. The stability and flexibility of the SFMI algorithm should be sufficient for most modeling applications until major improvements in other modeling factors are achieved. In addition, because of its balanced computational design, SFMI can easily be adapted to parallel computing architectures. SFMI thus should allow practical long-term integrations of global chemistry coupled to general circulation and climate models, studies of interannual and interdecadal variability in atmospheric composition, simulations of past multidecadal trends owing to anthropogenic emissions, long-term forecasting associated with projected emissions, and sensitivity analyses for a wide range of physical and chemical parameters. To carry out practical calculations, the earliest and most straightforward explicit approaches for solving atmospheric chemical rate equations were quickly abandoned in favor of numerical implicitness (or semi-implicitness), with or without iterative procedures to stabilize the solutions [e.g., see Shimazaki and Laird, 1970; Turco and Whirten, 1974]. At a given time step, species concentrations could be repeatedly calculated using a simple semi implicit form of (1) by updating the chemical production and loss rates using species concentrations calculated at the previous iteration. While this gener-1767

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Tests on combined projection/forward differencing integration for stiff photochemical family systems at long time step

Cited by 45 publications

References 58 publications

A Semi-implicit Numerical Scheme for Reacting Flow

A Semi-implicit Numerical Scheme for Reacting Flow

Aerosol‐induced chemical perturbations of stratospheric ozone: Three‐dimensional simulations and analysis of mechanisms

A new family Jacobian solver for global three‐dimensional modeling of atmospheric chemistry

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